In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM.

翻译：本文提出了一种基于预测校正的迭代卷积阈值法（ICTM），用于求解稳态热传导方程中的拓扑优化问题。该问题被表述为互补能量的约束最小化问题，包含周长/表面积正则化项，同时满足稳态热传导方程。优化问题的决策变量代表不同材料的区域，并通过指示函数表示。区域的周长/表面积项利用高斯核卷积与指示函数进行近似。在每次迭代中，指示函数通过预测校正方法更新。预测步骤基于施加约束后目标泛函的变分，而校正步骤确保目标泛函的单调递减行为。数值结果表明，所提方法具有高效性和鲁棒性，尤其在与基于经典ICTM的方法相比时优势显著。